'On the Pierce-Birkhoff Conjecture' -

*What real-valued functions can be expressed using addition, scalar multiplication and absolute value?* The answer is that any piecewise linear function (with finitely many pieces) \(f:\mathbb{R}^n\to \mathbb{R}\) can be expressed with these notational resources. How about the same question if we extend our notational resources by including multiplication? Evidently, any function that can be so expressed is piecewise polynomial. *Is it the case, conversely, that every piecewise polynomial function on* \(\mathbb{R}^n\) *can be so expressed?* The answer is *Yes* for \(n=1\) and \(n=2\), but remarkably we do not know the answer for \(n\geq 3\). In 1956, Garret Birkhoff and Richard Pierce conjectured *Yes, for all* *n*. This problem has had a significant impact on my career as a mathematician. In this talk, I'll sketch out important mathematics related to this problem and tell you about some of the people I've met and some of the experiences I've had while working on it.

James Madden graduated from Reed College in 1974 with a degree in Anthropol-ogy. He obtained his Ph.D. in Mathematics from Wesleyan University in 1983. He is presently the Patricia Hewlett Bodin Distinguished Professor of Mathematics at Louisiana State University.

Thursday, November 14, 2019 at 4:40pm to 5:30pm

Eliot Hall, 314

3203 Southeast Woodstock Boulevard, Portland, Oregon 97202-8199

- Department
- Mathematics, Division of Mathematical and Natural Sciences
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